Dear Authors,

I congratulate you to a clear and very carefully written paper.

Only a few tiny things should be corrected before I accept the manuscript. The page numbers refers to the marked up manuscript

1. It appears to me that units, in particular for t and delta t, are not consistently used throughout the paper. Even though your results are presented in normalised form, the variables t and delta are formally variables of unit time.
Captions of Figs. 4-6 correctly say t=h/u*. In many instances (also just above the inserted legends of the same figures) you write t=1, which seems incorrect to me. Could go over the whole manuscript and check for this?

2. p11, l14: citep instead of citet.

3. 15, l18: replace "will be" by "is"

4. In Figs 4-6, in partiucular the curve for the third order explicit scheme do not show results for the largest time steps. Why?

Best wishes,
Simon

Dear Authors

as already pointed out in my previous comment:
Congratulations to this nice piece of science.
It was a pleasure to edit this carefully written manuscript.

Best wishes,
Simon